“The Mankiw Rule” is what I call Greg Mankiw’s version of the
Taylor Rule. “Taylor
Rule” is now the general term for a rule that sets a monetary policy interest
rate (usually the federal funds rate in the US case) as a linear function of an
inflation rate and a measure of economic slack. ... Unfortunately, there are
now many different versions of the Taylor Rule, which all lead to different
conclusions. Not only are there many different measures of both slack and
inflation; there are also an infinite number of possible coefficients that could
be used to relate them to the policy interest rate. ...

Parsimony suggests that a good Taylor rule should have 3 characteristics: it
should be as simple as possible; it should use robust, easily defined, and
well-known measures of slack and inflation; and it should fit reasonably well to
past monetary policy. Also, to have credibility, such a rule should have “stood
the test of time” to some extent: it should fit reasonably well to some
subsequent monetary policy experience after it was first proposed. The Mankiw
Rule has all these characteristics. It uses the unemployment rate and the core
CPI inflation rate as its measures, and it applies the same coefficient to both.
This setup leaves it with only two free parameters, which Greg set in a 2001
paper (pdf)
so as to fit the results to actual 1990’s monetary policy. As you can see from
the chart below, the rule fits subsequent monetary policy rather well, although
policy has tended to be slightly more easy (until 2008) than the rule would
imply.

You will notice a
substantial divergence, however, after 2008, between the Mankiw Rule and the
actual federal funds rate. If the reason for this divergence isn’t immediately
clear, you need to take a closer look at the vertical axis. ...

If we wanted to make a guess as to when the Fed will (or should) raise its
target for the federal funds rate, a reasonable guess would be “when the Mankiw
Rule rate rises above zero.” When will that happen? (Will it ever happen?)
Nobody knows, of course, but the algebra is straightforward as to what will need
to happen to inflation and unemployment. If the core inflation rate remains near
1%, the unemployment rate will have to fall to 7%. If the core inflation rate
rises to 2%, the unemployment rate will still have to fall to 8%. Do you expect
either of these things to happen soon? I don’t.

I don't either, but that doesn't mean the Fed can't deviate from its past pattern. Let's hope that the members of the FOMC are smart enough not to begin raising interest rates too soon. However, the hawkish statements coming from the Fed recently, particularly from presidents of the regional Federal Reserve banks, do make me wonder if the Fed will begin raising rates while unemployment remains substantially elevated. For example (and this relatively dovish overall compared to, say, this):

The implication is that the policy rate may
have to begin to rise even while unemployment is considerably higher
than before the recession. I'm very concerned about unemployment, and
certainly employment trends should be a critical consideration in
setting policy. But I accept that good policy, even in circumstances of
unacceptable levels of unemployment, may incorporate higher interest
rates.

“The Mankiw Rule” is what I call Greg Mankiw’s version of the
Taylor Rule. “Taylor
Rule” is now the general term for a rule that sets a monetary policy interest
rate (usually the federal funds rate in the US case) as a linear function of an
inflation rate and a measure of economic slack. ... Unfortunately, there are
now many different versions of the Taylor Rule, which all lead to different
conclusions. Not only are there many different measures of both slack and
inflation; there are also an infinite number of possible coefficients that could
be used to relate them to the policy interest rate. ...

Parsimony suggests that a good Taylor rule should have 3 characteristics: it
should be as simple as possible; it should use robust, easily defined, and
well-known measures of slack and inflation; and it should fit reasonably well to
past monetary policy. Also, to have credibility, such a rule should have “stood
the test of time” to some extent: it should fit reasonably well to some
subsequent monetary policy experience after it was first proposed. The Mankiw
Rule has all these characteristics. It uses the unemployment rate and the core
CPI inflation rate as its measures, and it applies the same coefficient to both.
This setup leaves it with only two free parameters, which Greg set in a 2001
paper (pdf)
so as to fit the results to actual 1990’s monetary policy. As you can see from
the chart below, the rule fits subsequent monetary policy rather well, although
policy has tended to be slightly more easy (until 2008) than the rule would
imply.

You will notice a
substantial divergence, however, after 2008, between the Mankiw Rule and the
actual federal funds rate. If the reason for this divergence isn’t immediately
clear, you need to take a closer look at the vertical axis. ...

If we wanted to make a guess as to when the Fed will (or should) raise its
target for the federal funds rate, a reasonable guess would be “when the Mankiw
Rule rate rises above zero.” When will that happen? (Will it ever happen?)
Nobody knows, of course, but the algebra is straightforward as to what will need
to happen to inflation and unemployment. If the core inflation rate remains near
1%, the unemployment rate will have to fall to 7%. If the core inflation rate
rises to 2%, the unemployment rate will still have to fall to 8%. Do you expect
either of these things to happen soon? I don’t.

I don't either, but that doesn't mean the Fed can't deviate from its past pattern. Let's hope that the members of the FOMC are smart enough not to begin raising interest rates too soon. However, the hawkish statements coming from the Fed recently, particularly from presidents of the regional Federal Reserve banks, do make me wonder if the Fed will begin raising rates while unemployment remains substantially elevated. For example (and this relatively dovish overall compared to, say, this):

The implication is that the policy rate may
have to begin to rise even while unemployment is considerably higher
than before the recession. I'm very concerned about unemployment, and
certainly employment trends should be a critical consideration in
setting policy. But I accept that good policy, even in circumstances of
unacceptable levels of unemployment, may incorporate higher interest
rates.